We were always accustomed to have our young boys light the Menorah with wax candles until close of the age of bar mitzvah. It is easier and more fun for them to light using the wax candles and also easier for me the parent to set up. However, I am now wondering that perhaps they should light with olive oil as the best mitzvah is to light with olive oil
Certainly, from the letter of the law your children may light with wax candles, however it is encouraged for one to educate his child to perform the Mitzvah in the most scrupulous manner, and hence preferably olive oil should be used. But in the end of the day as a parent it is your decision of what you would prefer and also take the input of your child in the matter.
The question of whether children who are lighting Chanukah candles should be encouraged to use olive oil [which as we know is the best form of fuel to use for the Chanukah lights] versus wax, is dependent on whether children at all are obligated to light candles prior to reaching the age of bar mitzvah. This matter is disputed amongst the Poskim.
Some Poskim rule that according to the Ashkenazi custom for every household member to lights the candles, once a child reaches the age of Chinuch he is also required to light. Other Poskim however, rule that even according to the Ashkenazi custom in which all male household members light candles, nevertheless, there’s no obligation to educate a child in a matter of Hidur Mitzvah, and therefore he is not obligated to light. [Practically, according to Chabad custom, male children only begin lighting the Chanukah lights some time before their bar-mitzvah, as rules the 2nd opinion. Nevertheless, in many families of Anash, even very young children are educated to light their own candles. In the words of the Yesod Veshoresh Ha’avoda “One is to be very careful to educate his small sons to light their own Chanukah Menorah.”]
Now, according to the second opinion who holds that there is no obligation to be stringent to educate a child in a matter of Hiddur mitzvah, there is likewise no need to have a child use olive oil for the lighting. However, according to the first opinion who holds that the parents should educate his child a matter of Hiddur mitzvah, one can learn that one is to also educate his children to use olive oil. Practically, it is clear from the Achronim and documented Chabad custom, that there is no need to be particular for children to use olive oil. Nonetheless, as the Rebbe has encouraged us on many occasions, even children should be educated to fulfill Mitzvas on the highest of levels, which would include using olive oil for the Chanukah candles.
Sources: See regarding if children are obligated to light candles prior to the age of bar mitzvah: Yes: Rama 675:3 “According to our custom that every family member lights their own candles, also a child who has reached the age of education is required to light”; P”M 671 M”Z 1; See M”B 677:13; Kaf Hachaim 677:22; No: M”A 677:8 “Possibly even according to our custom that every family member lights their own candles, a child is exempt from lighting”; M”B 677:13; Biur Halacha 675:3 “Uledidon”; Shiltei Giborim, brought in M”A ibid; Meiri; Kaf Hachaim 677:22; The M”A and Biur Halacha ibid bring opinions that argue on Rama and hold that even according to the Ashkenazi custom that all male household members light, nevertheless, there’s no obligation to educate a child in a matter of Hidur Mitzvah, and therefore he is not obligated to light. The M”B 675:14 concludes he is only required to light one candle. According to Michaber, obviously the child does not light being that according to him only one person lights in each home. Chabad Custom: Sefer Haminhagim p. 157 [English] based on Sichas Chanukah 5706 that so is the custom by Beis Harav; This seemingly follows the latter opinion above. Shevach Hamoadim p.101; Hiskashrus; Perhaps this also follows a similar change in the later generation for girls to begin lighting Shabbat candles at a very young age; See Likkutei Sichos 12:251